Ideal-large subring

This article defines a property that can be evaluated for a unital subring in a commutative unital ring: given any commutative unital ring and a subring thereof, the property is either true or false for the pair
View a complete list of such properties

Definition

A unital subring of a commutative unital ring is said to be ideal-large if its intersection with any nonzero ideal of the whole ring is a nonzero ideal of the subring.

Facts

Any integral domain is ideal-large in any integral extension thereof.